Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case

被引：76
作者：
Brasco, Lorenzo [1 ,2 ]
Lindgren, Erik [3 ]
机构：
[1] Univ Ferrara, Dipartimento Matemat & Informat, Via Machiavelli 35, I-44121 Ferrara, Italy
[2] Aix Marseille Univ, CNRS, Cent Marseille, I2M,UMR 7373, 39 Rue Frederic Joliot Curie, F-13453 Marseille, France
[3] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden
来源：
ADVANCES IN MATHEMATICS | 2017年 / 304卷
关键词：
Fractional p-Laplacian; Nonlocal elliptic equations; Besov regularity;
D O I：
10.1016/j.aim.2016.03.039
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that for p >= 2, solutions of equations modeled by the fractional p-Laplacian improve their regularity on the scale of fractional Sobolev spaces. Moreover, under certain precise conditions, they are in W-loc(1,p) and their gradients are in a fractional Sobolev space as well. The relevant estimates are stable as the fractional order of differentiation s reaches 1. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：300 / 354
页数：57
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